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CivilComp Proceedings
ISSN 17593433 CCP: 96
PROCEEDINGS OF THE THIRTEENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping and Y. Tsompanakis
Paper 51
A Fast IncrementalIterative Procedure for Ultimate Strength Analysis and Design of Composite SteelConcrete CrossSections C.G. Chiorean
Faculty of Civil Engineering, Technical University of ClujNapoca, Romania C.G. Chiorean, "A Fast IncrementalIterative Procedure for Ultimate Strength Analysis and Design of Composite SteelConcrete CrossSections", in B.H.V. Topping, Y. Tsompanakis, (Editors), "Proceedings of the Thirteenth International Conference on Civil, Structural and Environmental Engineering Computing", CivilComp Press, Stirlingshire, UK, Paper 51, 2011. doi:10.4203/ccp.96.51
Keywords: interaction diagrams, rapid design, composite crosssections, ultimate strength analysis, arclength method, fully yield surfaces, biaxial bending.
Summary
The main objective of this paper is to present a new formulation by which the biaxial interaction diagrams and moment capacity contours of a composite steelconcrete crosssection can be determined, which make use of an incrementaliterative procedure based on arclength constraint equations. Furthermore, a new procedure based on a Newton iterative method is proposed to design the required reinforcement for sections subjected to axial force and biaxial bending moments.
The proposed method adopts a tangent stiffness strategy for the solution of the nonlinear equilibrium equations thus resulting in a high rate of convergence. Considering the solution of nonlinear equilibrium equations, involved in the evaluation of the interaction diagrams, the proposed incrementaliterative method is advantageous with respect to the existing ones [1,2,3]. The advantage is that the solution is obtained by solving just two coupled nonlinear equations and the convergence stability is not sensitive to the initial or starting values of the basic variables, involved in the iterative process, or to how the origin of the reference loading axes is chosen or to the strain softening effect for concrete in compression. The method proposed in the paper, for design of crosssections, consists of computing the required reinforcement area supposing that all structural parameters are specified and, under given external loads, the cross section reaches its failure either in tension or compression. The problem is formulated by means of three equilibrium equations for the section. The condition of ultimate limit state is enforced by a compatibility equation imposing the maximum strain on the section to be equal to the limit strain of the corresponding material. These nonlinear equations are manipulated so that one of them is uncoupled and the Newton iterative strategy is applied only to the remaining coupled equilibrium equations. The proposed approach is advantageous with respect to the existing ones [1,3], in that the solution is obtained by solving just three coupled nonlinear equations and the convergence stability is not sensitive to the initial or starting values of the basic variables involved in the iterative process. This method, as compared to other iterative methods used in the solution of nonlinear equations for the design of crosssections, is very stable, converging rapidly if the initial value of the required reinforcement area is properly selected. References
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